An existence theorem, with energy bounds, of Floer's perturbed Cauchy-Riemann equation with jumping discontinuity

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dc.creatorOh, Yong-Geun
dc.date2002-07-24
dc.date2003-11-18
dc.date.accessioned2026-07-07T04:49:48Z
dc.date.available2026-07-07T04:49:48Z
dc.descriptionThis is a sequel to the paper [Oh5] (or ArXiv:math.SG/0206092). The main purpose of the paper is to give the proof of an existence theorem, with energy bounds, of certain pseudo-holomorphic sections of the mapping cylinder that is needed for the proof of nondegeneracy of the homological invariant pseudo-norm which the author has constructed on general symplectic manifolds [Oh4,5]. The existence theorem is also the crux of the author's recent proof of an optimal energy-capacity inequality given in [Oh5]. In this paper, we prove a more general existence result than needed in that we study Floer's perturbed Cauchy-Riemann equations with discontinous Hamiltonian perturbation terms and prove an existence theorem of certain piecewise smooth finite energy solutions of the equation. The proof relies on a careful study of the product structure in the chain level Floer homology theory and a singular degeneration (``adiabatic degeneration'') of Floer's perturbed Cauchy-Riemann equation. In the course of the proof, we also derive certain general energy identity of pseudo-holomorphic sections of the Hamiltonian fibration.
dc.descriptiona sequel to the paper math.SG/0206092, the title slightly changed, the abstract and the introduction partly rewritten, and some details added and improved
dc.identifierhttps://arxiv.org/abs/math/0207214
dc.identifierhttp://arxiv.org/abs/math/0207214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64568
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.subject53D35, 53D40, 53D45
dc.titleAn existence theorem, with energy bounds, of Floer's perturbed Cauchy-Riemann equation with jumping discontinuity
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